System and method for transforming mission models from plan goal graph to bayesian network for autonomous system control

ABSTRACT

A method and system operable to perform the method is provided for control of an autonomous or unmanned system. The method includes obtaining a mission model, wherein the mission model comprises a goal and one or more assets that are used to accomplish the goal; producing, by a first hardware processor, a plan goal graph (PGG) model based on the mission model; transforming, by a second hardware processor, the PGG model into a Bayesian Network (BN) model; computing a feasibility to execute a plan and an achievability of accomplishing the goal; and providing control instructions to the one or more assets to be used to accomplish the goal.

FIELD

The present disclosure relates generally autonomous or semi-autonomouscyber or physical systems in which an automated method and system fortransforming mission models from Plan Goal Graph to Bayesian Network andfor automated reasoning based on the transformed models.

BACKGROUND

A Plan Goal Graph (PGG) represents plan-goal relationships in ahierarchical structure. Plans and goals are decomposed following theirmeans-ends relationships. A goal node in the PGG has plan nodes aschildren, which explicitly represent the alternative plans to achievethe goal. A plan node in the PGG has goal nodes as children, each ofwhich represents a sub-goal of the planned task, collectively definesthe objective of the plan. The leaf nodes are plan nodes correspondingto primitive actions that can be carried out in unit steps (e.g.,carrying out a sequence of steps to execute a pre-defined operation).

Bayesian network (BN) (also called belief networks, or causal networks)is a probabilistic graphical model that represents a set of randomvariables and their conditional dependencies via a directed acyclicgraph (DAG). A BN is a DAG where nodes represent random variables andedges represent conditional dependencies. Each node has an associatedconditional probability table (CPT) that quantifies the conditionalprobability distribution over the states of the node given differentcombinations of the states of the parent nodes.

Bayesian network has been increasingly used for representingprobabilistic knowledge. BN compactly represents the probabilisticdependencies among domain variables with the graphical structure. Thisquantified dependence representation provides a powerful reasoningplatform following the Bayes' Theorem. Efficient algorithms have beendeveloped to perform inference even with partial observation of variablestates. In a Bayesian network, the posterior probabilities of variablescan be computed given any other variables' state observations. Thenumerical value of posterior probabilities provides a quantitativeestimation of the possible states of the unobserved variables. In themission planning scenario, if the mission plans and goals arerepresented in Bayesian network models, the reasoning power of Bayesiannetworks can be used to evaluate the plans' feasibility and the goals'achievability.

Both PGG and BN are acyclic directed graph where nodes represent domainvariables and arcs represent dependence relationships between the nodes.In PGG, a node is either a plan node or a goal node. Arcs from a plannode to its sub-goal nodes indicates collective relationship among allthese sibling sub-goal nodes, i.e., all sub-goals must be met tocomplete the plan. Arcs from a goal node to its sub-plan nodes indicatesalternative relationships among all these sibling sub-plan nodes, i.e.,the goal may be met by choosing any of the plans.

By separating goals, plans, and sub-plans (i.e. actions to be performedto achieve the goals), a PGG is relatively easy for a person to createand understand. While PGG is an intuitive mission representation, it isinformal and provides no formal reasoning theoretical foundation andpractical mechanisms to compute probabilistic outcomes and based onwhich to reason and determine the course of actions. BN, on the otherhand, is a formal probabilistic reasoning model with a rigoroustheoretical foundation. Constructing a mission model in BN directly ischallenging for complex mission systems (e.g., mission execution byautonomous vehicles) because of its lack of intuitive notation ofplan-goal hierarchical decomposition.

Thus, a heretofore unaddressed need exists in the industry to addressthe aforementioned deficiencies and inadequacies.

SUMMARY

According to examples of the present disclosure, a method for control ofan autonomous or unmanned system is provided. The method comprisesobtaining a mission model, wherein the mission model comprises a goaland one or more assets that are used to accomplish the goal; producing,by a first hardware processor, a plan goal graph (PGG) model based onthe mission model; transforming, by a second hardware processor, the PGGmodel into a Bayesian Network (BN) model; computing a feasibility toexecute a plan and an achievability of accomplishing the goal; andproviding control instructions to the one or more assets to be used toaccomplish the goal.

In some examples, the one or more assets comprise an autonomous orunmanned system.

In some examples, the PGG comprises the goal represented as a firstparent node and one or more alternative plans to achieve the goalutilizing the one or more assets represented as one or more first childnodes to the first parent node, wherein the first parent node isconnected to each of the one or more first child nodes by one or morefirst directed arcs.

In some examples, the BN model comprises one or more alternative plansusing the one or more assets represented as one or more second parentnodes and the goal represented as a second child node to the one or moresecond parent nodes, wherein the one or more second parent nodes areconnected to the second child node by one or more second directed arcs.

In some examples, the transforming comprises changing a first directionof the first directed arcs to a second direction of the second directedarcs and adding a decision node to the second child node.

In some examples, the method further comprises defining one or moreachievability variables for one or more goal nodes, defining one or morefeasibility variables for one or more plan nodes, and a relationshipbetween the one or more feasibility variables for the one or more plannodes and the one or more achievability variables for the one or moregoal nodes.

In some examples, the method further comprises generating a conditionalprobability table for each node of the BN model that reflects aconditional probability distribution over one or more states of a nodegiven different combinations of the one or more states of each secondparent nodes. In particular, a goal's achievability is computed based ona combination of available plans and their feasibilities, and decisionsof selecting and executing those plans.

In some examples, the method further comprises adding a risk factor anda scaling factor in the computation of a plan's feasibility and a goal'sachievability.

In some examples, the BN model and a computation method of computing anachievability of a goal node and one or more feasibility variables forone or more plan nodes are embedded in a mission reasoning component ofan autonomous or semi-autonomous system to provide reasoning anddecisions based on computed best course of actions. In some examples,the computed best course of action can be the available plan with thehighest percentage of achieving the object of the goal based on one ormore factors including, but is not limited to, availability of resourcesof the asset(s), cost of use of the resources of the asset(s), andenvironmental factors such as the weather. In some example, the computedbest course can be the available plan with a percentage that meets acertain threshold of success, but not necessarily the course of actionwith the highest chance of success. If two different courses of actionboth meet the threshold, but the highest percentage course of action isimpacted by one or more of the above factors, the course of action withthe next highest percentage of success may be chosen.

In some examples, the first hardware processor and the second hardwareprocessor are the same or different processors.

In some examples, the one or more assets comprise a robot equipped withwired or wireless communication, anthropomorphic hands and limbs, and avision system. In some examples, the one or more assets comprise anautonomous air system, autonomous water system, or autonomous groundsystem. In some examples, the one or more assets comprise one or moreof: a wireless communication system, a cargo stowage unit, a materialhandling equipment unit, a vision system, or a global positioningsystem.

In accordance with the present disclosure, a computing system isprovided. The computing system comprises at least one hardwareprocessor; a non-transitory computer-readable storing instruction, thatwhen executed by the at least one hardware processor, perform a methodfor control of an autonomous or unmanned system, the method comprising:obtaining a mission model, wherein the mission model comprises a goaland one or more assets that are used to accomplish the goal; producing aplan goal graph (PGG) model based on the mission model; transforming thePGG model into a Bayesian Network (BN) model; computing a feasibility toexecute a plan and an achievability of accomplishing a goal; andproviding control instructions to the one or more assets to be used toaccomplish the goal.

To enable adaptive control that makes use of information that becomesknown during performance of a plan, in examples of the presentdisclosure, a PGG is translated into a BN that represents individualactions to be performed together with the observed probabilities ofsuccess and failure for the individual actions and the conditionalprobabilities of success and failure for the individual plans thatdepend upon certain environmental conditions or the outcome of certainother actions. A plan may be decomposed into sub-plans as combinationsof individual actions and other sub-plans together with the conditionalprobabilities of success and failure for the sub-plans based upon theirdependence on certain environmental conditions or the outcome of certainactions or certain other sub-plans.

By incorporating the relative probabilities of success and failure forindividual actions and the conditional probabilities of success andfailure for individual actions or sub-plans that depend uponenvironmental conditions or the outcome of other steps, a BN can be usedto guide the course of action according to environmental conditions andthe outcome of individual actions. Moreover, a BN can be used to guideincremental decisions to wait for more information, to wait for theoutcome of other actions, or to take action to obtain more information.

Examples of the present disclosure provides for operations including,but are not limited to, the following: 1) transforming large missionmodels in form of intuitive but informal PGG notations into formalBN-based mission models for intelligent reasoning in support of complex,dynamic and high-tempo mission operations; 2) reasoning about goalachievability, plan feasibility, and the best courses of actions priorto mission executions; 3) dynamically updating goal achievability andplan feasibility given partial observation or estimation duringsimulated or actual mission executions.

Examples consistent with the present disclosure provide for a system andmethod to automatically transform a PGG to a BN, which is then enhancedas needed and used for formal reasoning on mission goals, plans, andtheir achievability and feasibility, respectively. A PGG is ahierarchical decomposition of a mission goal into alternative plans toachieve the goal and a plan into sub-goals to meet the plan'sobjectives. The decomposition is a tree structure alternating betweengoals and plans starting from the overall mission goal as the root andending with the primitive plans as actionable unit steps. Thisdisclosure creates an automated method for transforming a PGG-basedmission representation to a BN-based mission representation and theresulting BN-based mission representation is then used for intelligentformal reasoning of mission goals, plans, and their achievability andfeasibility. This method provides the ability to create large missionmodels using intuitive but informal PGG notations and transform thePGG-based mission models into formal BN-based mission models forintelligent formal reasoning in support of complex, dynamic andhigh-tempo mission operations.

The present disclosure provides for, among other things, (1) anautomated transformation method from a PGG-based mission representationto a BN-based mission representation, (2) techniques for hierarchicallycomputing goal achievability and plan feasibility using the resultingBN-based mission representation, and (3) continuous inference of goalsand plans and keeping track of decisions and running estimate of goalachievability, plan feasibility with highlight of optimal paths in theBN-based graphical mission models.

Examples of the disclosure is applicable to examples of such systems asmission-critical command and control systems, cyber security defense andoffense systems, fault analysis and root cause diagnosis systems,decision systems, and emergency management systems. The systems mayinclude a robot equipped with wired or wireless communication,anthropomorphic hands and limbs, vision, etc. Moreover, the systems mayinclude unmanned, autonomous air, water, or ground vehicles or systemsequipped with wireless communication, cargo stowage, material handlingequipment, vision, global positioning systems (GPS), etc. Further, thesystem may be any autonomous system equipped to perform the actionsrequired to achieve a goal identified in a plan-goal-graph. Theautonomous system may be controlled remotely by a computer through wiredor wireless communication, or may be controlled locally by a computerphysically resident with or in the autonomous system. In each example,the autonomous system is controlled in accordance with a mission modelrepresented by a PGG or BN.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the implementations, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example of PGG modeling a mission to destroy enemytarget with an Apache helicopter and two UAVs with the goal of gettingthe Target Destroyed that can be achieved by either of two plans—Plan Ais to use one Apache two UAVs and Plan B is to use one Apache only,according to examples of the present disclosure.

FIG. 2 shows an example of an intermediate step of creating a BN from aPPG model, which is a fragment of a BN for the mission goal of getTarget Destroyed, according to examples of the present disclosure.

FIG. 3 shows a conditional probability table 300 for the TargetDestroyed goal node of FIG. 2 to represent the strength of thedependences, according to examples of the present disclosure.

FIG. 4 shows an automatic transformation method 400 of a PGG model andgeneration of a BN model, according to examples of the presentdisclosure.

FIG. 5 shows a PGG that represents a mission to destroy an enemy targetwith different choices of Apache helicopters and UAVs as availableresources, according to examples of the present disclosure.

FIG. 6 is the BN generated by transforming the PGG in FIG. 5.

FIG. 7 shows a method 700 for computing the conditional probability of agoal being Achieved given the feasibility of one of its plans is beingchosen, according to examples of the present disclosure.

FIG. 8 shows the conditional probability distribution of the goal nodeTarget Destroyed being Achieved that is computed given the feasibilityof the three plans and the selection of one of them using the MethodεRDC, according to examples of the present disclosure.

FIG. 9 shows the generated CPT 900 for the plan node One Apache Two UAVs(plan 1 805 from FIG. 8).

FIG. 10 shows the priori probability 1000 of the goal “Target Destroyed”and the feasibility of its three alternative child plans to achieve thegoal, according to examples of the present disclosure.

FIG. 11 illustrates the achievability of goal Target Destroyed when noplan is selected (i.e., all plans are equally likely to be chosen bydefault), according to examples of the present disclosure.

FIG. 12 illustrates the same variable when One Apache Two UAVs isselected as the plan to achieve the goal 1200, according to examples ofthe present disclosure.

FIG. 13 shows the probabilistic update of the plan One Apache Two UAVsaccording to its four sub-goals' state change, where all of itssub-goals have 49% probability to be achieved, and the plan'sfeasibility is also 49%.

FIG. 14 shows the probabilistic update of the plan One Apache Two UAVsaccording to its four sub-goals' state change, where when one of itssub-goals is known for sure being achieved (shown as 100% of thecorresponding state), then the plan's feasibility increases to 62%.

FIG. 15 shows an example of mission model development and transformationat the model generation time, and deployment and reasoning and operatorintelligent assistance at mission execution time, according to examplesof the present disclosure.

FIG. 16 show a material delivery scenario with the goal of deliveringpackage E1 to Location X, and package E2 to Location Y, both from theBase B, within timeliness and cost constraints, according to examples ofthe present disclosure.

FIG. 17 shows a PGG for the material delivery scenario of FIG. 16.

FIG. 18 shows a BN that has been transformed from the PGG of FIG. 17,according to the methods discussed herein.

FIG. 19 shows a conditioned probability table for the goal “‘Delivered”for the BN of FIG. 18.

FIG. 20 shows CPTs for different conditions for plan 1 of FIG. 18.

FIG. 21 shows CPTs 2100 and 2150 for different conditions for plan 2 ofFIG. 18.

FIG. 22 shows a graphic representation of a first example of BN of FIG.18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 23 shows a graphic representation of a second example of BN of FIG.18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 24 shows a graphic representation of a third example of BN of FIG.18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 25 shows a graphic representation of a fourth example of BN of FIG.18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 26 shows a graphic representation of a fifth example of BN of FIG.18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 27 shows a graphic representation of a sixth example of BN of FIG.18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 28 shows a graphic representation of a seventh example of BN ofFIG. 18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 29 shows a graphic representation of an eighth example of BN ofFIG. 18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown.

FIG. 30 shows a method for control of an autonomous or unmanned system,according to examples of the present disclosure.

FIG. 31 is an example computer system for performing the disclosedimplementations, consistent with the present disclosure.

DETAILED DESCRIPTION

Reference will now be made in detail to example implementations, whichare illustrated in the accompanying drawings. When appropriate, the samereference numbers are used throughout the drawings to refer to the sameor like parts.

For simplicity and illustrative purposes, the principles of the presentdisclosure are described by referring mainly to exemplaryimplementations thereof. However, one of ordinary skill in the art wouldreadily recognize that the same principles are equally applicable to,and can be implemented in, all types of information and systems, andthat any such variations do not depart from the true spirit and scope ofthe present disclosure. Moreover, in the following detailed description,references are made to the accompanying figures, which illustratespecific exemplary implementations. Electrical, mechanical, logical andstructural changes may be made to the exemplary implementations withoutdeparting from the spirit and scope of the present disclosure. Thefollowing detailed description is, therefore, not to be taken in alimiting sense and the scope of the present disclosure is defined by theappended claims and their equivalents.

Generally speaking, examples of the present disclosure provide for anautomated system and method configured to transform mission models inPGG-based representation to corresponding models in BN-basedrepresentation for mission planning an execution for one or more assetsincluding, but are not limited to manned systems and unmanned system(e.g., unmanned aerial vehicles (UAVs), unmanned aerial systems (UASs),unmanned ground vehicles (UGVs)). In some examples, the one or moreassets comprise a robot equipped with wired or wireless communication,anthropomorphic hands and limbs, and a vision system. In some examples,the one or more assets comprise an autonomous air system, autonomouswater system, or autonomous ground system. In some examples, the one ormore assets comprise one or more of: a wireless communication system, acargo stowage unit, a material handling equipment unit, a vision system,or a global positioning system.

Additionally, methods for quantitatively computing goal achievabilityand plan feasibility based on BN reasoning theories and formulas areprovided. The transformation method and the achievability/feasibilitycomputation algorithms further enable runtime reasoning in support ofmission execution. The method, algorithms, and reasoning capability canbe embedded in a variety of applications for automated oroperator-in-the-loop complex mission systems. The automatedtransformation of mission models in PGG-based representation tocorresponding models in BN-based representation preserves the structureand semantics of the mission model in PGG-based representation byreversing the parent-child relations between goals and plans, augmentsthe basic structure of the BN-based model generated by thetransformation method by adding a decision node in the BN for each goalnode and linking the decision node as an additional parent to the goalnode, and generates the state space and determine the probability ofeach state for each decision node. Moreover, conditional probabilitiescan be determined and assigned in each node's CPT. Furthermore, thegoal's achievability and plan's feasibility can be computed recursivelyacross the structure of the generated BN-based mission model based onsound BN reasoning theories and formulas. The methods, algorithms, andreasoning capabilities can be embedded in a variety of applications forautomated or operator-in-the-loop complex mission systems and canprovide continuous running estimate of plan's feasibility and goal'sachievability during mission execution based on the generated missionmodels in BN-based representation.

In a typical PGG-based mission model, the ultimate goal of a mission isrepresented as a root node in the PGG and the goal is decomposed intoalternative plans, each of which when carried out will achieve the goal.If a plan is not a primitive action that can be directly carried out, itis further decomposed into a set of sub-goals, all of which must beachieved in order to execute the plan. A Course of Action (COA) is asequence of chosen plans that eventually achieve the mission goal at theroot of a PGG. In this disclosure, the terms task and plan are usedinterchangeably.

One advantage of using PGG for mission representation is that itexplicitly separates goals and plans (tasks). This distinction providesan intuitive mechanism to represent complex missions as a decompositionof a goal to alternative plans and a plan to a set of sub-goals.Conversely, a PGG-based model may be used as a basis to infer theoperator's intent when tracking his/her actions that are linked tohigher level of goals and plans.

However, one disadvantage of PGG is that it does not have a formalreasoning methodology for mathematically rigorous and theoreticallysound inference. For instance, PGG does not define any methodology toaddress reasoning issues such as how to compute a goal's achievabilitygiven its child plans' feasibility (as probability of success), andsimilarly, how to compute a plan's feasibility given its sub-goals'achievability, and how to compute and recommend a COA that has the bestprobability of success based on the plans' feasibility and goals'achievability. With BN, the probabilistic dependencies can berepresented explicitly and quantitatively in a directed acyclic graphwith conditional probability tables. This representation allows forbelief update to compute the nondeterministic plan feasibility and goalachievability.

In short, PGG is an intuitive model to represent hierarchical plan-goalrelationships explicitly, but lacks formal methods to represent andreason quantitative properties (e.g., probability of success) of plans,goals, dependencies and constraints. FIG. 1 shows an example of PGGmodeling a mission to destroy enemy target with an Apache helicopter andtwo UAVs 100 with the goal of getting the Target Destroyed 102 that canbe achieved by either of two plans, according to examples of the presentdisclosure. The first plan is to only use one Apache 104 and the secondplan is to use one Apache together with two UAVs 106. Both plans 104,106 can be decomposed into four sub-goals: Target Located 108, 116,Target Approached 110, 118, Target Attacked 112, 120, and BDA Assessed114, 122. These sub-goals each can be achieved by its decomposed plans.For example, in first plan of “One Apache” 104, the goal of TargetLocated 108 can be achieved by the means of a plan or primitive actionto request it from a Command and Control center (C2) 124. The goal ofTarget Attacked 118 can be achieved by means of Fire from Apache 134.The goal of Target Approached 120 can be achieved by means of Fly Apacheto Target 130. The goal of BDA Assessed 122 can be achieved by means ofGet BDA from C2 142. For the second plan using “One Apache Two UAVs”106, the goal of Target Located 108 can also be additionally achieved bythe means of a plan or primitive action to acquire the target by UAV,which is represented by the plan node Acquire By UAV 126. The goal ofTarget Approached 110 can be achieved by means of Fly UAV to Target 128,Fly Apache to Target 130, or Fly All to Target 132. The goal of TargetAttacked 112 can be achieved by means of Fire from Apache 134 or Firefrom UAV 136. The goal of BDA Assessed 114 can be achieved by means ofAssess BDA by UAV 138, Assess BDA by Apache 140, or Get BDA from C2 142.

Note the layered structure of PGG, starting with the mission goal at thetop layer (root of the PGG tree), e.g., the node for Target Destroyed102. The second layer is the plan nodes as children of the goal node inthe first layer, e.g., the nodes for the first plan to use one Apache104 and the node for the second plan is to use one Apache together withtwo UAVs 106. The third layer is the sub goal nodes, the children of theplan nodes in the second layer, so on so forth, e.g., the nodes forTarget Located 108, 116, Target Approached 110, 118, Target Attacked112, 120, and BDA Assessed 114, 122.

FIG. 2 shows an example of a BN 200, which is an intermediate constructgenerated from the PGG of FIG. 1 by the disclosed PGG to BN modeltransformation method. The BN 200 is a fragment of a BN for the missiongoal of get Target Destroyed 202, according to examples of the presentdisclosure. In this simplified network, the Target Destroyed goal node202 is the child of two plans that can achieve this goal, i.e., the planinvolving one Apache and one UAV 204 and the plan involving one Apacheand two UAVs 206. The two plans 204, 206 are divided into foursub-goals: Target Located 208, Target Approached 210, Target Attacked212, and BDA Assessed 214. The achievability of the goal depends on thesuccess of the plans when executed. The parent-child relationship in theBN follows the causal relationship. If one of the plans is successfullycarried out, then the goal will be highly likely achieved and themission will be complete. FIG. 3 shows a conditional probability table300 for the Target Destroyed goal node 202 of FIG. 2 to represent thestrength of the dependences, according to examples of the presentdisclosure.

One disadvantage of BN is the complexity of model construction. BuildingBayesian networks for complex mission scenarios, especially forautonomous cyber or physical systems, requires major investment in notonly modeling domain knowledge, but also understanding BN theory andtechniques. Tools are developed to facilitate the Bayesian networkmodeling. However, compared with PGG, constructing a mission model in BNis not as intuitive as in PGG.

To combine the advantages of easy construction of PGGs and powerfulreasoning capability of BNs, this disclosure provides a system andmethod to transform PGGs to BNs automatically. This method transformsconcepts and constructs in a PGG to concepts and constructs in a BN. Thetransformation preserves the semantics of the concepts of goals andplans and their relationships in PGG and adds extensions for formalreasoning on goals, plans, and course of actions. In addition,constructs not present in PGG are automated added and fused to theinitial BN model transformed from the PGG model. Furthermore, formalrelationships of goal's Achievability and Plan's Feasibility are definedand incorporated in the initial BN model transformed from the PGG model.Computation of the goal's Achievability and Plan's Feasibility is alsocreated in the initial BN model transformed from the PGG model. Finally,the reasoning capability using the BN model is enhanced to provideintelligent decision support to mission operators or autonomous decisionmaking using quantitative feasibility and achievability computationsbased on BN's rigorous conditional probability theory. The method forgraphical structure transformation and the conditional probabilitydistribution estimation is described below.

A PGG starts with a goal node and spans its graph structure with one ormore plans as children nodes. Each plan node spans the graph structurefurther with multiple sub-goal nodes. Recursively, the goal-planstructure and plan-goal structure specify the hierarchical decompositionof abstract goals or plans into concrete tasks or actions. The leafnodes of the PGG tree structure are the primitive tasks or actions thata machine or a human operator can carry out. The relationship as an arcbetween a parent node and a child node in PGG, i.e., between a goal anda plan to achieve the goal or between a plan and a sub-goal to beachieved, is a decomposition relationship.

When transforming a PGG structure to a BN structure, the graphicalstructure is preserved including concepts, constructs, and theirsemantics. This structure preserving feature is an element of ourinnovation method.

FIG. 4 shows an automatic transformation method 400 of a PGG model andgeneration of a BN model, according to examples of the presentdisclosure. The transformation takes two logical steps. The method 400begins by reversing, at 405, the directions for all arcs so that arelationship A->B in the PGG becomes a relationship B->A in itscounterpart BN. One insight of the arc direction reversion is that thedecomposition relationship between a parent node and a child node in PGGis semantically equivalent to a dependency relationship between themwhere the parent's success, measured as a plan's feasibility or a goal'sachievability for example, depends on the child's success. For instance,a goal's achievability depends on all its alternate plans'feasibilities. And similarly, a plan's feasibility depends on all itssub-goals' achievability. The reversion of the arcs' directions followsthe causal relationships among plans and goals for explicit and compactrepresentation in the BN model.

Another insight of the arc direction reversion is that the leaf nodes ofthe PGG are the primitive tasks whose feasibilities are determined byenvironmental factors other than goals and other plans represented inthe PGG/BN mission models. Their chances of success are independent ofother nodes in the mission models. Therefore, in BN model, these nodesshould be parentless nodes and their CPTs simply represent the priorprobabilities of their states (i.e., success or failure) respectively.

Yet another insight of the arc direction reversion is that the goalnodes and plan nodes in PGG represent mission goals and decomposableplans whose success often involves uncertainty rather than completelydeterministic. The reversion of the arc directions helps reduce thecomplexity of the resulted BN model both in terms of structure and inconditional probability tables. It helps minimize the number ofparameters to encode the CPTs.

The method 400 continues by augmenting, at 415, the basic structure ofthe BN generated at 410. The augmenting at 415 can be subdivided into420 and 415, where, at 420, a decision node is added in the BN for eachgoal node and link the decision node as an additional parent to the goalnode (technically, the resulting BN is an Influence Diagram, but isstill called BN for simplicity). The reason for doing this is torepresent plan choices made by human operators, as goal achievabilitydepends on the selected plans. Keep in mind that a goal may be achievedby multiple plans (e.g., in an alternate relationship). In the PGG, thegoal is the parent of these plans. In the BN, these plans are the parentof the goal node. The addition of decision nodes is automated, one foreach goal node, in this step.

Then, at 425, once decision nodes are added to the BN, the state spaceis generated and the probability of each state for each decision node isdetermined. The number of the possible states of the decision nodeequals to the number of the child plans for the goal which is the childof the decision node. The i^(th) state of the decision node indicatesthe i^(th) child plan being selected by human operators. The decisionnode is a deterministic node representing the scenario that, when one ofits states is selected, the corresponding plan would be chosen tofulfill the goal. By default, each plan has equal probability beingselected among all alternate sibling plans. The method 400 continues bygenerating, at 430, the Conditional Probability Tables (CPT) for thenodes in the BN, which is further described below. The method 400concludes by generating, at 435, the mission model in BN.

FIG. 5 shows a PGG 500 that represents a mission to destroy an enemytarget with different choices of Apache helicopters and UAVs asavailable resources, according to examples of the present disclosure.The PGG 500 include three plans to accomplish the goal of targetdestroyed 502. The first plan is to use one Apache and two UAVs 504, allto be deployed to destroy the enemy target. The second plan is to useone Apache and one UAV 506. The third plan is to use only one Apachewithout a UAV 508. Each plan has four sub-goals respectively, namely,Target Located 510, 518, 526, Target Approached 512, 522, TargetAttacked 514, 520, and BDS Assessed 516, 524. As can be seen, all threeaction plans are children nodes of the Target Destroyed goal node 502(the root of the PGG), each of the three plan nodes has four childrennodes corresponding to the four sub-goal nodes. In FIG. 5, the plannodes are one Apache two UAVs 504, one Apache one UAV 506, one Apache508, Request from C2 528, Acquire by UAV 530, Fly UAV to Target 532, FlyApache to Target 534, Fly All to Target 536, Fire from Apache 538, Firefrom UAV 540, Assess BDA by UAV 542, Assess BDA by Apache 544, AssignManually 564, Assign by DTA 566, Receive from UAV 568, ReceiveConfirmation 570, Receive Confirmation 572, Confirm Target 574, ConfirmReadiness 576, Fire Weapon 578, and Confirm Readiness 580. The goalnodes are Target Located 510, Target Approached 512, Target Attacked514, BDS Assessed 516, Target Located 518, Target Attacked 520, TargetApproached 522, BDS Assessed 524, Target Located 526, UAV Assigned 546,Target Received 548, UAV Confirmed 550, UAV Confirmed 552, Weapon Ready554, Target Confirmed 556, Weapon Fired 558, Weapon Ready 560, andWeapon Fired 562. Note that the figure only shows a partial picture ofthe PGG structure.

FIG. 6 is the BN generated by transforming the PGG in FIG. 5. Note thatthe graph structure is upside down compared with the original PGG withreversions of the parent-children relationship. The constructs ofdecision nodes as parents to the goal nodes are then added and fusedinto the model. The addition of decision nodes is an important part ofthe transformation. The figure only shows a partial picture of the BNstructure for illustration. In FIG. 6, same as in PGG, the plan nodesare Request from C2 602, Flay Apache to Target 604, Assign Manually 606,Assign by DTA 608, UAV Report Target Location 610, Receive Confirmation612, Receive Confirmation from UAV 614, Confirm Target 616, Acquire byUAV 634, Fly UAV to Target 636, Fly All to Target 638, Fire from Apache640, Fire from UAV 642, Assess BDA by UAV 644, Assess BDA by Apache 646,Get BDA from C2 648, one Apache two UAVs 664, one Apache one UAV 666,and one Apache 668. The goal nodes are Target Located 618, TargetApproached 620, UAV Assigned 622, Target Received 624, UAV Confirmed626, UAV Confirmed 628, Weapon Ready 630, Target Confirmed 632, TargetLocated 650, Target Approached 652, Target Attacked 654, BDA Assessed656, Target Located 658, Target Attacked 660, and BDA Assessed 662.These nodes are all random variables in oval shape. The decision nodesare rectangular nodes, i.e., Target Destroyed Decision 670. The rootgoal node is Target Destroyed 672. The arcs point from parents tochildren to indicate their causal effectual relationships.

Beside the graph structure, a BN has another important part: ConditionalProbability Distributions (CPD). In a BN, a parentless node is definedwith a prior probability distribution function (for continuousvariables) or table (for discrete variables). A node having parents isrepresented with a conditional probability function or table whichdefines the probabilities of the variable given the joint states of itsparents. In this disclosure, the method of generating CPD only ondiscrete variables is illustrated and thus only Conditional ProbabilityTables (CPT) are needed.

Typically in a PGG, nodes are discrete variables, therefore, in thisdisclosure, the focus is on how to generate Conditional ProbabilityTables (CPT) for discrete variables. Furthermore, the terms “node” and“variable” are used interchangeably to simplify the description of theapproach.

Returning to FIG. 4, the CPT are generated, at 430, for BN-based missionmodel, as shown in FIG. 6. Note that a node's CPT represents the jointstates of all possible combinations of its parent states and the node'sown state. Due to this multidimensional and combinatorial nature, itrequires exponential number of parameters to populate a CPT. For abinary state node with n binary state parents, the number of parametersin its CPT is 2′. (A binary state node is a node with two states, e.g.,yes/no, achieved/failed).

To illustrate the power of automatic BN model generations, the focus ison the capability of automatically assessing plan feasibility and goalachievability. For simplicity, goals and plans are modeled as binarystate nodes in BN. A goal node has two states: Achieved or Failed; aplan node has two states: Feasible and Infeasible. For a goal N_(G) withm alternative child plans N (i=1, 2, . . . m) to achieve the goal, itsparent decision node has m number states. When the goal and plans aremodeled as binary state nodes, its CPT is an m+2 dimensional table, andit requires m*2^(m+1) number of probability parameters.

When generating the CPT table for a goal node N_(G), uncertainties areintroduced such that when a plan N_(Pi) is feasible and chosen to becarried out, the achievability of N_(G), takes a probability value 1−ε,where ε represents any unexpected factors to prevent the goal from beingachieved after the plan is executed. In other words, ε represents aninherent mission risk factor. Clearly, when such uncertainty does notexist, let ε=0. For simplicity of discussion, ε is assumed to be aconstant.

By definition of the model, a goal may be achieved by selecting any ofthe plans, provided a selected plan is Feasible. FIG. 7 shows a method700 for computing the conditional probability of a goal being Achievedgiven the feasibility of one of its plans is being chosen, according toexamples of the present disclosure. The method 700 begins byconfiguring, at 705, operation parameters that impact the inherent riskfactor ε as the probability of a plan that is Feasible but still couldfail when it is executed. Select methods to compute the inherent riskfactor ε based on the operation parameters.

The method 700 continues by computing, at 710, an inherent risk factor εfor each plan. It is obvious that when the plan is Infeasible, ε=1,i.e., 100% of fail probability. If the plan is Feasible, the computationof ε can be done in multiple automated methods. As an example, a method(termed “Method εRDC”) is to assess the redundancies in a plan—the moreredundant assets used in a plan, the less risk to fail—in comparison ofmaximum redundancies in all plans for achieving a goal. In this examplemethod, the operation parameters are the max number of assets in amission and the available redundant assets in a particular plan. Asanother example, a method (termed “Method εCPX”) is to estimate thecomplexity of a plan by means of the number of assets that must becoordinated. The more complex, the more risk and thus higher ε value. Inthis example method, the operation parameter are the number of assetsand the complexity of coordination among them in a mission. The computedε value may be manually adjusted by operator.

The method 700 concludes by computing, at 715, a goal's probabilitydistribution of being Achieved as 1−ε under each condition of a plan ischosen and whether the plan is Feasible or Infeasible, where ε is thecomputed risk factor of the plan computed in 710.

To demonstrate the process of computing the conditional probabilitydistribution, the goal of Target Destroyed and its three sub-plans areused as an example. As shown in FIG. 8, the conditional probabilitydistribution 800 of the goal node Target Destroyed being Achieved iscomputed given the feasibility of the three plans and the selection ofone of them using the Method εRDC. The risk factor ε is first computedas the conditional probability when the goal is Failed but a Feasibleplan is selected using a function of (number of available redundanciesof assets to execute a plan):(1+((total number of available redundanciesof assets)−(number of redundancies of assets to execute the selectedplan))*θ, where θ is a scaling factor for the goal. The scaling factorfor many goals may be the same, but some goals may have differentscaling factors, as determined by the operators. Then the conditionalprobability when the goal is Achieved is apparently 1−ε. On the otherhand, as mentioned earlier, the risk factor ε is always 1 when anInfeasible is selected to execute, and hence the conditional probabilityis 0 for the goal being Achieved when an infeasible plan is selected(regardless the feasibility of other plans).

For example, assume the scaling factor θ is determined as 1% by theoperator. In the following, the conditional probabilities are computedwhen all the three plans are Feasible for each of the three cases whereeach plan is selected to execute. Note that here the maximum number ofavailable assets is 3: one Apache plus two UAVs. In this example, themethod εRDC is selected to compute the risk factor ε.

Plan 1805: One Apache Two UAVs is chosen to be executed: here the numberof available redundant assets to execute Plan 1 is 3. Hence,ε=(1+(3−3))*0.01=0.01.

Therefore, the conditional probability of the goal node Target Destroyedbeing Achieved when all plans are Feasible and Plan 1 805: One ApacheTwo UAVs chosen to be executed is 1−ε=1−0.01=0.99. Plan 2 810: OneApache One UAV is chosen to be executed: here the number of availableredundant assets to execute Plan 2 810 is 2 (as 1 of the 2 UAVs is notavailable). For this Plan 2 810, ε=(1+(3−2))*0.01=0.02.

Therefore, the conditional probability of the goal node Target Destroyedbeing Achieved when all plans are Feasible and Plan 2 810: One ApacheOne UAV is chosen to be executed is 1−ε=1−0.02=0.98.

Plan 3 815: One Apache is chosen to be executed: here the number ofavailable redundant assets to execute Plan 3 is 1 (the Apache). For thisPlan 3 815, ε=(1+(3−1))*0.01=0.03.

Therefore, the conditional probability of the goal node Target Destroyedbeing Achieved when all plans are Feasible and Plan 3 815: One Apache ischosen to be executed is 1−ε=1−0.03=0.97.

In this example, the feasibility of un-selected plan does not play arole in the computation. For example, the conditional probability of thegoal node Target Destroyed being Achieved when Plan 1 805 is Feasibleand chosen to be executed while Plan 2 810 or Plan 3 815 is Infeasibleis the same: 0.99. Apparently, using this approach, the operators onlyneed to determine the scaling factor θ for each goal as they developmission plans. The exponential number of probabilities in theconditional probability table is determined automatically using thealgorithm described above.

Alternative methods may be used to compute the ε for each plan and thevalue of ε may be adjusted by operators manually through means directchange or via a parameterized input table. As noted earlier, a plan isnot feasible but chosen to achieve its goal, then ε=1 and theachievability of the goal should be zero. The CPT cells corresponding tosuch cases have values of 0 for Achieved state and 1 for Failed outcome,as shown in FIG. 8.

In summary, when generating CPT for a goal node, the default CPT valuesare computed conditioned on each of its feasible plans consistent withits decision parent's choice state. When a parent plan is in itsFeasible state and the parent decision node is in a state of choosingthis plan, the goal's state of being Achieved is computed as probabilityvalue 1−ε, where ε is a computed risk factor of executing the plan; whena parent plan is in its Infeasible state but the parent decision node isin a state of choosing this plan, then the goal's state of beingAchieved is zero probability value because ε=1.

In generating CPT for a plan node, the CPT values are assigned in aquite different way. The probability of a plan's Feasible state equalsto the ratio of its Achieved sub-goals out of the total number of theplan's sub-goals.

In a BN, a plan node has its supported sub-goals as its parent nodesafter transforming from the original PGG. For a plan node N_(p) withN_(Si) (i=1, . . . , m) sub-goal parent nodes, its CPT has m+1dimensions and requires 2^(m+1) number of probability parameters. Whenall of the sub-goals are in the state of being Achieved, then the planmust be 100% feasible and its corresponding CPT cell takes value of 1.When k out of m sub-goals are Achieved, then the plan has k/mprobability being feasible. When none of the sub-goals can be achieved,then the plan's feasibility is zero. FIG. 9 shows the generated CPT 900for the plan node One Apache Two UAVs (plan 1 805 from FIG. 8).

The method of FIG. 7 can be used to generate default CPTs for theBN-based mission model. The generated model may be updated by domainexperts through graphical tools.

With the BN representation of the dependencies among plans and goals,and an operator's choice of alternative plans, the operator can beprovided with a quantified assessment on the chance of success ofvarious choices. The plan feasibility and goal achievability aredynamically computed, driven by external events and operator decisions.For plan feasibility, the computation is a bottom-up belief propagationstarting from setting the state of leaf plans (primitive actions whosefeasibility can be determined by various external influential factorsuch as resource availability and communication capability for a missionexecution). The goal achievability depends on its alternative childplans and is computed based on the child plans' feasibility update.These belief updates are propagated up to the root goal throughplan-goal layers and the ultimate goal feasibility can be assessed oncethe belief propagation is completed. The operator can immediately seethe estimated rate of mission success from the Bayesian reasoningresult. Comparing the rate for each alternative plan choices, theoperator can easily pick the best plan for achieve the goal. Thisprocess can easily be performed autonomously when operator interventionis not required.

A state-of-the-art BN inference algorithm can be used for computation ofplan feasibility and goal achievability. In the BN models generatedusing the present methods, the layered structure of PGG is kept, theobservable states of primitive action plans are set as evidences toinfer the posterior probabilities for estimating achievability of thegoal nodes and feasibility of the plan nodes. When no evidence ispresent, a priori probabilities are computed for the estimation. FIG. 10shows the priori probability 1000 of the goal “Target Destroyed” and thefeasibility of its three alternative child plans to achieve the goal,according to examples of the present disclosure. Note that the successand failure rates are roughly equal, about 50%. The plan “One Apache TwoUAVs” 1005 has a little lower feasibility compared to other two plans,e.g., the plan “One Apache One UAV” 1010 and the plan “One Apache” 1015,as it requires more resources (i.e., two UAVs) that may result in higherrisk of resource being unavailable.

When reasoning with BN for achievability of a goal G, G's marginalprobability p(G) is computed. The calculation follows Bayes' Theorem bysumming out of its parent variables (P1, P2, . . . Pn). This process iscalled marginalization. Here p(G) is used to represent the probabilityof Goal G being in the Achieved state, p(G=Achieved), and p(P) torepresent the probability of Plan P being in the Feasible state,p(P=Feasible). The p(G=Failed) is the complement of the p(G=Achieved),therefore p(G=Failed)=1−p(G=Achieved). For the plan node, the complementrelationship holds true for the Infeasible state and Feasible state:p(P=Infeasible)=1−p(P=Feasible).

When no decision is made on plan choices, each plan is treated withequal chance of being selected, all plans have the same influence on thegoal's achievability.

${p(G)} = {\sum\limits_{{P\; 1},\ldots \;,{Pn}}{{p\left( {\left. G \middle| {P\; 1} \right.,{\ldots \mspace{14mu} {Pn}}} \right)}{p\left( {{P\; 1},{\ldots \mspace{14mu} {Pn}}} \right)}}}$

When a decision is made on plan choices, the goal's achievabilitydepends on the selected plan's feasibility. The unselected plans won'thave any effect to the goal's achievability in this situation.

FIG. 11 illustrates the achievability 1100 of goal Target Destroyed whenno plan is selected, p(Target Destroyed)=26%.

FIG. 12 illustrates the same variable when One Apache Two UAVs isselected as the plan to achieve the goal 1200, according to examples ofthe present disclosure. As can be seen, under this situation, p(TargetDestroyed)=p(One Apache Two UAVs)=31%. In FIG. 12, the first state,ONE_Apache_Two_UAV 1205 of the Target_Destroyed_decision node 1210 isthe selected plan.

Note that both estimated values for the goal achievability are low, 26%and 31%. This is because all the involved plans' feasibilities are lowin the given situations, as they depend on the upper layer nodes' stateand their corresponding probabilities, which ultimately depend on thefirst layer nodes, i.e., the primitive action nodes. In the illustratedsettings, those action nodes were not set to favor the feasible state.They have equal chance of being feasible or infeasible. These nodes arenot shown in the figures for simplified illustration of probabilitydependency among the goal node Target Destroyed and its plans anddecision nodes.

Similar to the assessment of goal achievability, the assessment of planassessment also follows Bayes' Theorem. For a plan node P with n goalnode parents G1, . . . Gn, its probability is the marginal sum out ofthe goals' probability.

${p(P)} = {\sum\limits_{{G\; 1},\ldots \;,{Gn}}{{p\left( {\left. P \middle| {G\; 1} \right.,{\ldots \mspace{14mu} {Gn}}} \right)}{p\left( {{G\; 1},{\ldots \mspace{14mu} {Gn}}} \right)}}}$

When sub-goals are achieved with certain probability, their parentplan's feasibility can be computed and updated accordingly. Generally,increase of the sub-goals' achievability will increase the plan'sfeasibility. When all sub-goals are known (100% certain) to be achieved,the plan's feasibility is 100%.

FIG. 13 and FIG. 14 show the probabilistic update of the plan One ApacheTwo UAVs according to its four sub-goals' state change. In FIG. 13, allof its sub-goals have 49% probability to be achieved, and the plan'sfeasibility is also 49%. In FIG. 14, when one of its sub-goals is knowfor sure being achieved (shown as 100% of the corresponding state), thenthe plan's feasibility increases to 62%. The more certain its sub-goalsget achieved, the greater the parent plan's feasibility is.

The methods described herein of automatically transforming missionmodels in PGG-based representation to corresponding models in BN-basedrepresentation and providing runtime reasoning in support of missionexecution can be embedded in a variety of applications. For example,mission models in BN can be dynamically loaded and embedded in a MissionAssociate application, providing intelligent assistance to the operator.FIG. 15 shows an example of mission model development and transformationat the model time, and deployment and reasoning and operator intelligentassistance at mission execution time 1500, according to examples of thepresent disclosure. An operator 1505 can execute an application 1510,e.g., a mission associate application, on a computer (not shown), i.e.,a smart phone, laptop, tablet computer, desktop computer. Theapplication 1510 can communicate with a control system 1520 and canobtain mission events 1515 from the operator 1505, the control system1520, or another party. The control system 1520 provides a mission modelin the form of a PGG 1525. The mission model in PGG is converted to a BN1530. The mission model in BN is enhanced with probabilities of successbased on domain knowledge 1535 and is provided to an inference engine1540, which can then be provided to the application 1510. The missionmodel can be updated as needed using, for example, domain experts. Theoperator 1505 can make appropriate selection on the application 1510,which can then be provided to the inference engine 1540.

FIGS. 16-29 show an example material delivery scenario using the methodsdescribed herein, according to examples of the present disclosure. Thematerial delivery can include, but is not limited to, medicine/parceldelivery in wild mountain ranges without good transportationinfrastructure, emergency kits distribution after disaster whereinfrastructures are destroyed, routine outpost supply refilling frombases in Mars colony, or UGV parts and tools to assembly large factory.The above examples may include material pickup in addition to delivery.FIG. 16 show a material delivery scenario 1600 with the goal ofdelivering package E1 to Location X 1610, and package E2 to Location Y1615, both from the Base B 1605, within timeliness and cost constraints.In this example, the resources and plans options include the following:available resources—two UAVs for simplicity, assuming identicalcapability); plan options—use one or two UAVs; and depends on packages'weights, weather condition (wind speeds, lightening, heavy rain/snow),and timeliness guarantees, it might be more or less feasible for a UAVto delivery one or two packages via a specific route segments at ascheduled delivery time. Also for this example, the environment andconditions include the following: base B 1605 is closer to Location X1610 than to Location Y 1615 and Location X 1610 and Location Y 1615 arecloser to each other than to Base B 1605; and weather conditions.

FIG. 17 shows a PGG 1700 for the material delivery scenario of FIG. 16.The goal 1705 of this scenario is that the packaged is delivered and theUAV(s) returned within timeliness guarantees. Plan 1 (P1) 1710 is twoUAVs working concurrently, each delivers one package to one location andflies back. In particular, P1 1710 is a first UAV (UAV 1) being taskedwith proceeding from Base B 1605 to Location X 1610 and then back Base B1605, which is represented as UAV1:B→X→B. A second UAV (UAV2) is taskedwith proceeding from Base B 1605 to Location Y 1615 and then back toBase 1605, which is represented as UAV2: B→Y→B. Plan 2 (P2) 1715 is oneUAV, from base B to location X, then to location Y then back to B (UAVx:B→X→Y→B). Plan 3 (P3) 1720 is one UAV, from base B to location Y, thento location X then back to B (UAVx: B→Y→X→B). It is possible to use asingle UAV; B→X→B→Y→B, or B→Y→B→X→B, but this is ignored in these plansfor simplicity. Bottom level sub-goals B→X 1725, X→Y 1730, Y→B 1735, B→Y1740, Y→B 1745, and Y→X 1750 can be further decomposed, but the purposehere is to use a simple example to illustrate details described herein.As a result (for simplicity), it is assumed that their feasibility canbe observed (or calculated externally) and hence treated as actions.

FIG. 18 shows a BN 1800 that has been transformed from the PGG of FIG.17, according to the methods discussed herein. The goal nodes includeB→X 1805, X→Y 1810, Y→B 1815, B→Y 1820, Y→X 1825, and X→B 1830 and theplan nodes include P1: B→X→Y 1835, P2: B→Y→B 1840, and P3: B→Y→X 1845.The goal node 1850 is delivered and retuned and the decision node is theautomated plan selection 1865. The probability of success for theprimary goal node 1850 (delivered) is conditional (dependent) on theprobability of success of the alternative plans P1: B→X→Y 1835, P2:B→Y→B 1840, and P3: B→Y→X 1845. A BN may also contain sequentialdependencies between parentless nodes that are not directly representedin the hierarchical node & arrow representation. For example, in plan P21840, there is sequential dependency between B→X 1805 and X→Y 1810 andthe probability of success for X→Y 1810 is conditional (dependent) onthe probability of success for B→X 1805. FIG. 19 shows a CPT 1900 forthe goal “‘Delivered” for the BN of FIG. 18.

FIG. 20 shows CPTs 2000 and 2050 for different conditions for plan 1 ofFIG. 18. If there are sequential dependency on the sub-goals, all thesub-goals are partitioned from the same plan node into N parallel groupsof sequential ones (B→X and X→B forms 1^(st) group, while B→Y and Y→Bforms 2^(nd) group, N=2 in this example). Each group, if fully achieved,contributes 1/N to the plan feasibility. Within the group of K sub-goals(K=2 in this example), each sub-goal contribute to 1/K of the groupcontribution. In addition, the failure of a sub-goal will reduce itssubsequent sibling sub-goals' contribution to a ratio ρ (say 80% in thisexample, in general, like ε, the ratio can be a configurable constantdetermine by human experts during mission planning). For example,failure of B→X reduce the contribution of X→B, but does not reduce thecontribution of B→Y or Y→B

FIG. 21 shows CPTs 2100 and 2150 for different conditions for plan 2 ofFIG. 18. Using the analysis of the preceding paragraph, a single groupof K=3 sub-goals is considered. Consider column 3 (AFA in sequence), B→Xachieved contributes ⅓, Y→B achieved contributes ⅓ but reduced to(⅓)*80%= 4/15. Hence total contribution is ⅓+ 4/15= 9/15=0.6. Considercolumn 7 (FFA), Y→B achieved contributes ⅓ but reduced twice by 80%*80%=16/25, and hence total contribution is ⅓*( 16/25)= 16/75.

FIG. 22 shows a graphic representation of a first example of BN 1800 ofFIG. 18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown. In this example, noconsideration of a sequential order is considered and no additionalinformation is considered. The outcome of each top row plan is equallyweighted A:50% F:50%, the plan probabilities calculated, the choice ofplans are equally weighted, which results in a probability that the goalis achieved calculated to be 53%.

When no plan is selected as shown in FIG. 22, the achievability of thegoal is the averaged value from three different options where one planis selected in each option. FIG. 23 shows a graphic representation of asecond example of BN 1800 of FIG. 18 with the calculation of initialprobabilities, propagation and calculation of conditional probabilitiesshown. In this example, no consideration of a sequential order isconsider and the route between X and Y is considered to be blocked, asshown in the 100% failure condition between X->Y and X->Y. When theroute between X->Y is blocked, either P2 or P3 can only carry out ⅓ andhence their feasibility is 33%. The top row plan probability and theplan probabilities updated based on these conditions. The choice ofplans are equally weighted, which results in a probability that the goalis achieved calculated to be 42%.

FIG. 24 shows a graphic representation of a third example of BN 1800 ofFIG. 18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown. In this example, noconsideration of a sequential order is consider and the route between Xand Y is considered to be blocked, similar to that as discussed in FIG.23. The top row plan probability and the plan probabilities updatedbased on these conditions. Also, in this example, plan P2 is consider,which results in a probability that the goal is achieved calculated tobe 33%.

FIG. 25 shows a graphic representation of a fourth example of BN 1800 ofFIG. 18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown. In this example, noconsideration of a sequential order is consider and the route between Xand Y is considered to be blocked, similar to that as discussed in FIG.23. The top row plan probability and plan P1 is consider. Since plan P1does not depend on X->Y route, P1 has a much higher feasibility (but not100% as B->X and B->Y route still has uncertainty). This results in aprobability that the goal is achieved calculated to be 62%.

In the examples of FIGS. 22-25, the feasibility of all plans are reducedslightly due to sequential dependency. For example, when B->X fails inthese examples, it does not change the contribution to P1 for theAchieved X->Y. However, in the below example, it does. FIG. 26 shows agraphic representation of a fifth example of BN 1800 of FIG. 18 with thecalculation of initial probabilities, propagation and calculation ofconditional probabilities shown. In this example, sequential order isconsider and no other information is considered. The outcome of each toprow plan is equally weighted A: 50% F: 50%, the plan probabilities arecalculated (taking into consideration sequential order), and the choiceof plans equally weighted. This results in a probability that the goalis achieved calculated to be 45%.

FIG. 27 shows a graphic representation of a sixth example of BN 1800 ofFIG. 18 with the calculation of initial probabilities, propagation andcalculation of conditional probabilities shown. In this example,sequential order is consider and the route between X and Y is consideredto be blocked, similar to that as discussed in FIG. 23. The top row planprobability is updated and the choice of plans is equally weighted. Thisresults in a probability that the goal is achieved calculated to be 34%.

FIG. 28 shows a graphic representation of a seventh example of BN 1800of FIG. 18 with the calculation of initial probabilities, propagationand calculation of conditional probabilities shown. In this example,sequential order is consider and the route between X and Y is consideredto be blocked, similar to that as discussed in FIG. 23. The planprobabilities are updated and plan P2 is considered. This results in aprobability that the goal is achieved calculated to be 28%.

FIG. 29 shows a graphic representation of an eighth example of BN 1800of FIG. 18 with the calculation of initial probabilities, propagationand calculation of conditional probabilities shown. In this example,sequential order is consider and the route between X and Y is consideredto be blocked, similar to that as discussed in FIG. 23. The top row planprobability is updated, the plan probabilities are updated, and plan P1is considered. This results in a probability that the goal is achievedcalculated to be 47%.

In some examples, the above described systems and method can be used inan autonomous system control. The autonomous system control can accept aPGG and control parameters (ρ and ε) from a command center and cantransform the PGG to a BN with conditional probability table using thecontrol parameters. The autonomous system control can be configured toset initial probabilities of achieved to 50% for each parentless node(at top) in the BN and then to calculate the probabilistic of othernodes via BN propagation. The autonomous system control can beconfigured to use the pseudocode below:

Repeat Perform routine mission execution logic «e.g., situationassessment, acquiring information, evaluating the effect of alternativesub-plans, . . . Etc.» Wait pre-determined duration of time for newinformation If (new information available) then Update BN with newinformation Compute the probabilities of a Plan's Feasibility and aGoal's Achievability Determine the possible effect of selectingalternative sub-plans (including atomic actions) on the probability of aGoal's Achievability Update recommended course of actions (i.e.,sequence of alternative sub-plans) based on new probabilities End If If(Action is required) then Perform selected sequence of alternativesub-plans Determine outcome Update BN with outcome End If RepeatThe process can be repeated until the plan completes or is infeasible tocontinue.

In some examples, the autonomous system control can be configured with abackup configuration. In the backup configuration, all external factorscan be aggregated into a single environmental condition factor for eachof the three route segment (B←→X, B←→Y, X←→Y). As one example, theenvironment can be represented by an event that can be detected by aweather service and provided to the mission. The event can becharacterized in conditions, e.g., [Favorable, Prohibitive, Workable].When the environment is Favorable, both packages may be carried in asingle UAB. When the environment is Prohibitive, no UAV can fly acrossthe segment. Otherwise, the environment is Workable, only a singlepackage may be carried in a single UAV. Note that there is always asmall chance that the UAV may fail due to unforeseen conditions. In someexamples, different environmental condition can be assigned fordifferent route segment.

In some examples, the autonomous system control can include autonomousdecision making. In this example, external events are some of the inputin the decision loop. If, for example, the weather conditions havechanged, a plan could be B->X, X->B, B->Y rather than B->X->Y->B. Inother words, alternative plans can be consider to achieve the same goal.Other considerations can include timeliness and cost for a givencondition (defined as the set of events, UAV conditions, etc.). In someexamples, a human out-of-loop process can use external events to provideevidence to the BNN, where the achievability of the goal under eachdecision choice can be determined and can automatically take the choicewith the maximum achievability.

FIG. 30 shows a method 3000 for control of an autonomous or unmannedsystem, according to examples of the present disclosure. The method 3000begins by obtaining, at 3005, a mission model, wherein the mission modelcomprises a goal and one or more assets that are used to accomplish thegoal. In some examples, the one or more assets can comprise anautonomous or unmanned system. In some examples, the one or more assetscan comprise a robot equipped with wired or wireless communication,anthropomorphic hands and limbs, and a vision system. In some example,the one or more assets can comprise an autonomous air system, autonomouswater system, or autonomous ground system. In some examples, the one ormore assets can comprise one or more of: a wireless communicationsystem, a cargo stowage unit, a material handling equipment unit, avision system, or a global positioning system.

In some example, the PGG comprises the goal represented as a firstparent node and one or more alternative plans to achieve the goalutilizing the one or more assets represented as one or more first childnodes to the first parent node, wherein the first parent node isconnected to each of the one or more first child nodes by one or morefirst directed arcs.

In some example, the BN model comprises on or more alternative plansusing the one or more assets represented as one or more second parentnodes and the goal represented as a second child node to the one or moresecond parent nodes, wherein the one or more second parent nodes areconnected to the second child node by one or more second directed arcs.

The method 3000 continues by producing, at 3010, by a first hardwareprocessor, a plan goal graph (PGG) model based on the mission model. Themethod 3000 continues by transforming, at 3015, by a second hardwareprocessor, the PGG model into a Bayesian Network (BN) model. In someexamples, the transforming comprises changing a first direction of thefirst directed arcs to a second direction of the second directed arcsand adding a decision node to the second child node. The method 3000continues by computing, at 3020, a feasibility to execute a plan and anachievability of accomplishing the goal. The method 3000 continues byproviding, at 3025, control instructions to the one or more assets to beused to accomplish the goal.

In some example, the method 3000 can further comprise defining one ormore achievability variables for one or more goal nodes, defining one ormore feasibility variables for one or more plan nodes, and arelationship between the one or more feasibility for the one or moreplan nodes and the one or more achievability variables for the one ormore goal nodes.

In some examples, the method 3000 can further comprise generating aconditional probability table for each node of the BN model thatreflects a conditional probability distribution over one or more statesof a node given different combinations of the one or more states of eachsecond parent nodes. For example, a goal's achievability is computedbased on a combination of available plans and their feasibilities, anddecisions of selecting and executing those plans.

In some examples, the method 3000 can further comprise adding a riskfactor and a scaling factor in the computation of a plan's feasibilityand a goal's achievability.

In some examples, the BN model and a computation method of computing anachievability of a goal node and one or more feasibility variables forone or more plan nodes are embedded in a mission reasoning component ofan autonomous or semi-autonomous system to provide reasoning anddecisions based on computed best course of actions.

In some example, the first hardware processor and the second hardwareprocessor can be the same or different processors.

FIG. 31 is an example computer system 3100 for performing the disclosedimplementations, consistent with the present disclosure. The computerdevice 3100 can be any type of computer devices, such as desktops,laptops, servers, etc., or mobile devices, such as smart telephones,tablet computers, cellular telephones, personal digital assistants, etc.As illustrated in FIG. 31, the computer device 3100 can include one ormore processors 3102 of varying core configurations and clockfrequencies. The computer device 3100 can also include one or morememory devices 3104 that serve as a main memory during the operation ofthe computer device 3100. For example, during operation, a copy of thesoftware that supports the operations discussed herein can be stored inthe one or more memory devices 3104. The computer device 3100 can alsoinclude one or more peripheral interfaces 3106, such as keyboards, mice,touchpads, computer screens, touchscreens, etc., for enabling humaninteraction with and manipulation of the computer device 3100.

The computer device 3100 can also include one or more network interfaces3108 for communicating via one or more networks, such as Ethernetadapters, wireless transceivers, or serial network components, forcommunicating over wired or wireless media using protocols. The computerdevice 3100 can also include one or more storage device 3110 of varyingphysical dimensions and storage capacities, such as flash drives, harddrives, random access memory, etc., for storing data, such as images,files, and program instructions for execution by the one or moreprocessors 3102.

Additionally, the computer device 3100 can include one or more softwareprograms 3112 that enable the functionality described above. The one ormore software programs 3112 can include instructions that cause the oneor more processors 3102 to perform the processes described herein.Copies of the one or more software programs 3112 can be stored in theone or more memory devices 3104 and/or on in the one or more storagedevices 3110. Likewise, the data used by one or more software programs3112 can be stored in the one or more memory devices 3104 and/or on inthe one or more storage devices 3110.

In implementations, the computer device 3100 can communicate with otherdevices via a network 3116. The other devices can be any types ofdevices as described above. The network 3116 can be any type ofelectronic network, such as a local area network, a wide-area network, avirtual private network, the Internet, an intranet, an extranet, apublic switched telephone network, an infrared network, a wirelessnetwork, and any combination thereof. The network 3116 can supportcommunications using any of a variety of commercially-availableprotocols, such as TCP/IP, UDP, OSI, FTP, UPnP, NFS, CIFS, AppleTalk,and the like. The network 3116 can be, for example, a local areanetwork, a wide-area network, a virtual private network, the Internet,an intranet, an extranet, a public switched telephone network, aninfrared network, a wireless network, and any combination thereof.

The computer device 3100 can include a variety of data stores and othermemory and storage media as discussed above. These can reside in avariety of locations, such as on a storage medium local to (and/orresident in) one or more of the computers or remote from any or all ofthe computers across the network. In some implementations, informationcan reside in a storage-area network (“SAN”) familiar to those skilledin the art. Similarly, any necessary files for performing the functionsattributed to the computers, servers, or other network devices may bestored locally and/or remotely, as appropriate.

In implementations, the components of the computer device 3100 asdescribed above need not be enclosed within a single enclosure or evenlocated in close proximity to one another. Those skilled in the art willappreciate that the above-described componentry are examples only, asthe computer device 3100 can include any type of hardware componentry,including any necessary accompanying firmware or software, forperforming the disclosed implementations. The computer device 3100 canalso be implemented in part or in whole by electronic circuit componentsor processors, such as application-specific integrated circuits (ASICs)or field-programmable gate arrays (FPGAs).

If implemented in software, the functions can be stored on ortransmitted over a computer-readable medium as one or more instructionsor code. Computer-readable media includes both tangible, non-transitorycomputer storage media and communication media including any medium thatfacilitates transfer of a computer program from one place to another. Astorage media can be any available tangible, non-transitory media thatcan be accessed by a computer. By way of example, and not limitation,such tangible, non-transitory computer-readable media can comprise RAM,ROM, flash memory, EEPROM, CD-ROM or other optical disk storage,magnetic disk storage or other magnetic storage devices, or any othermedium that can be used to carry or store desired program code in theform of instructions or data structures and that can be accessed by acomputer. Disk and disc, as used herein, includes CD, laser disc,optical disc, DVD, floppy disk and Blu-ray disc where disks usuallyreproduce data magnetically, while discs reproduce data optically withlasers. Also, any connection is properly termed a computer-readablemedium. For example, if the software is transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition of medium.Combinations of the above should also be included within the scope ofcomputer-readable media.

The foregoing description is illustrative, and variations inconfiguration and implementation can occur to persons skilled in theart. For instance, the various illustrative logics, logical blocks,modules, and circuits described in connection with the embodimentsdisclosed herein can be implemented or performed with a general purposeprocessor, a digital signal processor (DSP), an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA) orother programmable logic device, discrete gate or transistor logic,discrete hardware components, or any combination thereof designed toperform the functions described herein. A general-purpose processor canbe a microprocessor, but, in the alternative, the processor can be anyconventional processor, controller, microcontroller, or state machine. Aprocessor can also be implemented as a combination of computing devices,e.g., a combination of a DSP and a microprocessor, a plurality ofmicroprocessors, one or more microprocessors in conjunction with a DSPcore, or any other such configuration.

In one or more exemplary embodiments, the functions described can beimplemented in hardware, software, firmware, or any combination thereof.For a software implementation, the techniques described herein can beimplemented with modules (e.g., procedures, functions, subprograms,programs, routines, subroutines, modules, software packages, classes,and so on) that perform the functions described herein. A module can becoupled to another module or a hardware circuit by passing and/orreceiving information, data, arguments, parameters, or memory contents.Information, arguments, parameters, data, or the like can be passed,forwarded, or transmitted using any suitable means including memorysharing, message passing, token passing, network transmission, and thelike. The software codes can be stored in memory units and executed byprocessors. The memory unit can be implemented within the processor orexternal to the processor, in which case it can be communicativelycoupled to the processor via various means as is known in the art.

While the teachings have been described with reference to examples ofthe implementations thereof, those skilled in the art will be able tomake various modifications to the described implementations withoutdeparting from the true spirit and scope. The terms and descriptionsused herein are set forth by way of illustration only and are not meantas limitations. In particular, although the processes have beendescribed by examples, the stages of the processes can be performed in adifferent order than illustrated or simultaneously. Furthermore, to theextent that the terms “including”, “includes”, “having”, “has”, “with”,or variants thereof are used in the detailed description, such terms areintended to be inclusive in a manner similar to the term “comprising.”As used herein, the terms “one or more of” and “at least one of” withrespect to a listing of items such as, for example, A and B, means Aalone, B alone, or A and B. Further, unless specified otherwise, theterm “set” should be interpreted as “one or more.” Also, the term“couple” or “couples” is intended to mean either an indirect or directconnection. Thus, if a first device couples to a second device, thatconnection can be through a direct connection, or through an indirectconnection via other devices, components, and connections.

Those skilled in the art will be able to make various modifications tothe described embodiments without departing from the true spirit andscope. The terms and descriptions used herein are set forth by way ofillustration only and are not meant as limitations. In particular,although the method has been described by examples, the steps of themethod can be performed in a different order than illustrated orsimultaneously. Those skilled in the art will recognize that these andother variations are possible within the spirit and scope as defined inthe following claims and their equivalents.

The foregoing description of the disclosure, along with its associatedembodiments, has been presented for purposes of illustration only. It isnot exhaustive and does not limit the disclosure to the precise formdisclosed. Those skilled in the art will appreciate from the foregoingdescription that modifications and variations are possible in light ofthe above teachings or may be acquired from practicing the disclosure.For example, the steps described need not be performed in the samesequence discussed or with the same degree of separation. Likewisevarious steps may be omitted, repeated, or combined, as necessary, toachieve the same or similar objectives. Similarly, the systems describedneed not necessarily include all parts described in the embodiments, andmay also include other parts not describe in the embodiments.

Accordingly, the disclosure is not limited to the above-describedembodiments, but instead is defined by the appended claims in light oftheir full scope of equivalents.

What is claimed is:
 1. A method for control of an autonomous or unmannedsystem comprising: obtaining (3005) a mission model, wherein the missionmodel comprises a goal and one or more assets that are used toaccomplish the goal; producing (3010), by a first hardware processor(3102), a plan goal graph (PGG) model (100) based on the mission model;transforming (3015), by a second hardware processor (3102), the PGGmodel into a Bayesian Network (BN) model (200); computing (3020) afeasibility to execute a plan and an achievability of accomplishing thegoal; and providing (3025) control instructions to the one or moreassets to be used to accomplish the goal.
 2. The method of claim 1,wherein the one or more assets (104, 106) comprise an autonomous orunmanned system.
 3. The method of claim 1, wherein the PGG (100)comprises the goal represented as a first parent node and one or morealternative plans to achieve the goal utilizing the one or more assetsrepresented as one or more first child nodes to the first parent node,wherein the first parent node is connected to each of the one or morefirst child nodes by one or more first directed arcs.
 4. The method ofclaim 3, wherein the BN model (200) comprises one or more alternativeplans using the one or more assets represented as one or more secondparent nodes and the goal represented as a second child node to the oneor more second parent nodes, wherein the one or more second parent nodesare connected to the second child node by one or more second directedarcs.
 5. The method of claim 4, wherein the transforming (3015)comprises changing (410) a first direction of the first directed arcs toa second direction of the second directed arcs and adding a decisionnode to the second child node.
 6. The method of claim 5, furthercomprising defining one or more achievability variables for one or moregoal nodes, defining one or more feasibility variables for one or moreplan nodes, and a relationship between the one or more feasibilityvariables for the one or more plan nodes and the one or moreachievability variables for the one or more goal nodes.
 7. The method ofclaim 5, further comprising generating a conditional probability table(430) for each node of the BN model that reflects a conditionalprobability distribution over one or more states of a node givendifferent combinations of one or more states of each second parentnodes.
 8. The method of claim 5, further comprising adding a risk factorand a scaling factor in the computing the feasibility and theachievability.
 9. The method of claim 1, wherein the BN model (200) anda computation method of computing an achievability of a goal node andone or more feasibility variables for one or more plan nodes areembedded in a mission reasoning component of an autonomous orsemi-autonomous system to provide reasoning and decisions based oncomputed best course of actions.
 10. The method of claim 1, wherein thefirst hardware processor and the second hardware processor are differentprocessors.
 11. The method of claim 1, wherein the one or more assetscomprise a robot equipped with wired or wireless communication,anthropomorphic hands and limbs, and a vision system.
 12. The method ofclaim 1, wherein the one or more assets comprise an autonomous airsystem, autonomous water system, or autonomous ground system.
 13. Themethod of claim 1, wherein the one or more assets comprise one or moreof: a wireless communication system, a cargo stowage unit, a materialhandling equipment unit, a vision system, or a global positioningsystem.
 14. A computing system (3100) comprising: at least one hardwareprocessor (3102); a non-transitory computer-readable medium (3104, 3110)storing instruction, that when executed by the at least one hardwareprocessor, perform a method for control of an autonomous or unmannedsystem, the method comprising: obtaining (3005) a mission model, whereinthe mission model comprises a goal and one or more assets that are usedto accomplish the goal; producing (3010) a plan goal graph (PGG) model(100) based on the mission model; transforming (3015) the PGG model intoa Bayesian Network (BN) model (200); computing (3020) a feasibility toexecute a plan and an achievability of accomplishing the goal; andproviding (3025) control instructions to the one or more assets to beused to accomplish the goal.
 15. The computing system of claim 14,wherein the one or more assets (104, 106) comprise an autonomous orunmanned system.
 16. The computing system of claim 14, wherein the PGG(100) comprises the goal represented as a first parent node and one ormore alternative plans to achieve the goal utilizing the one or moreassets represented as one or more first child nodes to the first parentnode, wherein the first parent node is connected to each of the one ormore first child nodes by one or more first directed arcs.
 17. Thecomputing system of claim 16, wherein the BN model (200) comprises oneor more alternative plans using the one or more assets represented asone or more second parent nodes and the goal represented as a secondchild node to the one or more second parent nodes, wherein the one ormore second parent nodes are connected to the second child node by oneor more second directed arcs.
 18. The computing system of claim 17,wherein the transforming (3015) comprises changing (410) a firstdirection of the first directed arcs to a second direction of the seconddirected arcs and adding a decision node to the second child node. 19.The computing system of claim 18, wherein the at least one hardwareprocessor is operable to perform the method further comprising definingone or more achievability variables for one or more goal nodes, definingone or more feasibility variables for one or more plan nodes, and arelationship between the one or more feasibility variables for the oneor more plan nodes and the one or more achievability variables for theone or more goal nodes.
 20. The computing system of claim 18, whereinthe at least one hardware processor is operable to perform the methodfurther comprising generating a conditional probability table (430) foreach node of the BN model that reflects a conditional probabilitydistribution over one or more states of a node given differentcombinations of one or more states of each second parent nodes.
 21. Thecomputing system of claim 14, wherein the BN model and a computationmethod of computing an achievability of a goal node and one or morefeasibility variables for one or more plan nodes are embedded in amission reasoning component of an autonomous or semi-autonomous systemto provide reasoning and decisions based on computed best course ofactions.
 22. The computing system of claim 14, wherein the computingsystem comprises the autonomous or the unmanned system.
 23. Thecomputing system of claim 14, wherein the computing system is a systemthat is separate from the autonomous or the unmanned system.